Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
Generally, the measurement and reference beams are derived from a common source. Typically, the source delivers an input beam to the interferometer, which splits the input beam into the measurement and reference beams. In some embodiments, one or more optical waveguides are used to deliver the input beam, or components of the input beam, from the light source to the interferometer.
In many applications, the measurement and reference beams have orthogonal polarizations. In certain applications, the measurement and reference beams can have different frequencies as well. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarization beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams.
A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/λ, where v is the relative speed of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the phase of the measured interference signal correspond to changes in the relative position of the measurement object, e.g., a change in phase of 2π corresponds substantially to a distance change L of λ/(2np). Distance 2L is a round-trip distance change or the change in distance to and from a stage that includes the measurement object. In other words, the phase Φ, ideally, is directly proportional to L, and can be expressed asΦ=2pkL cos2θ  (1)
for a plane mirror interferometer, e.g., a high stability plane mirror interferometer, where
  k  =            2      ⁢                          ⁢      π      ⁢                          ⁢      n        λ  and θ is the orientation of the measurement object with respect to a nominal axis of the interferometer. This axis can be determined from the orientation of the measurement object where Φ is maximized.